To find the derivative of the function
y=√sinx+y, we will use implicit differentiation. Given the function:
y=√sinx+yFirst, square both sides to eliminate the square root:
y2=sinx+yNext, differentiate both sides with respect to
x. Remember to use the chain rule and implicit differentiation for
y :
(y2)=(sinx+y) Using the chain rule on the left side, we get:
2y=cosx+Now, isolate
:
2y−=cosx(2y−1)=cosx=Now, substitute
x=0 and
y=1 into the equation:
|x=0,y=1=Since
cos(0)=1|x=0,y=1=|x=0,y=1=So, the derivative
at
x=0 and
y=1 is 1 . Hence, the correct answer is:
Option B: 1